How is xex and xe2x integrated manually?

Answer 1

The definite integral of the function f=x*exp(k*x) is (1/k)*(x-(1/k))*exp(k*x). So you have the answer to your questions by setting k equal to 1 then 2.

I derived my formula by using integration by parts, setting u=x and dv=exp(k*x)dx.